Problem: $\dfrac{5}{6} \div \dfrac{9}{4} = {?}$
Answer: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $\dfrac{9}{4}$ is $\dfrac{4}{9}$. Therefore: $ \dfrac{5}{6} \div \dfrac{9}{4} = \dfrac{5}{6} \times \dfrac{4}{9} $ $ \phantom{\dfrac{5}{6} \times \dfrac{4}{9}} = \dfrac{5 \times 4}{6 \times 9} $ $ \phantom{\dfrac{5}{6} \times \dfrac{4}{9}} = \dfrac{20}{54} $ $ \phantom{\dfrac{8}{3} \times \dfrac{3}{5}} = \dfrac{10}{27} $